To begin with a preface, suppose that the following sentence occurs in the preface of a book:
All the sentences in this book are true.That sentence is clearly there to say that all the other sentences in that book are true. So, it would make sense for us to take that sentence to be true if all the others are. It would be silly to say that it was not true on the grounds that it might be false (because if it is false then not all the sentences are true). But what about the following sentence:
This sentence is true.Sentences like that are called Truth-Tellers, because sentences like "this sentence is not true" are called Liars. Now, that Truth-Teller is saying only that what it is saying is true, so it is certainly not saying much. It is unlike the sentence in that preface, in that respect; although in other ways, the two are very similar: it is consistent for the Truth-Teller to be true, and consistent for it to be false. Still, there is not much for it to be true or false about, so it is hard to think of it as being very true or very false. And there seems to be no way of determining which it is, in any case. Could we say that it was not very true and not very false? Could we say that it is about as true as not (and about as false as not)?
......To see why that might be possible, consider a man going bald. As he goes bald, he will not, by the loss of just one or two hairs, become bald, so there might be an intermediate stage at which he is about as bald as not, when it would make sense for it to be about as true as not that he was bald (and about as false as not). Perhaps it will help to look at the following sentence, which occurs in the preface of a work of fiction:
None of the sentences in this book are true.If that sentence – let us call it Disclaimer – was true, none of the sentences in that book would be true, so Disclaimer would not be true. By reductio ad absurdum, that means that Disclaimer is not true. So, either it is false – in which case at least one of the other sentences would have to be true (and we can assume that none of them are) – or else Disclaimer is neither true nor false. And Disclaimer did not seem to be meaningless. Are we stuck? Hardly. Disclaimer was presumably there to inform us that none of the other sentences in that book were true. If none of them were, then Disclaimer was, in that sense, true. And how could it have had any other meaning?
